Chapter 6: Applications of DifferentiationMarch 14, 2024 Maven Leave a Comment Welcome to the Chapter 6: Applications of Differentiation Name Email 1. Average cost is minimum when Marginal cost = Marginal revenue Average cost = Marginal cost Average cost = Marginal revenue Average Revenue = Marginal cost None 2. The demand function is always Increasing function Decreasing function Non-decreasing function Undefined function None 3. If q=$1000+8p_{1}-p_{2}$, then $\frac{\partial q}{\partial p_{1}}$ is -1 8 1000 $1000- p_{2}$ None 4. If u$=x^{3}+3xy^{2}+y^{3}$, then $\frac{\partial ^{2}u}{\partial x\partial y}$ is equal to 3 6y 6x 2 None 5. If u$=4x^{2}+4xy+y^{2}+4x+32y+16$, then $\frac{\partial ^{2}u}{\partial x\partial y}$ is equal to 8x + 4y + 4 4 2y + 32 0 None 6. If f(x,y) is a homogeneous function of degree n, then $x\frac{\partial f}{\partial x} + y \frac{\partial f}{\partial y}$ is equal to (n–1)f n(n–1)f nf f None 7. If u$=e^{x^{2}}$, then $\frac{\partial u}{\partial x}$ is equal to $2xe^{x^{2}}$ $e^{x^{2}}$ $2e^{x^{2}}$ 0 None 8. A company begins to earn profit at Maximum point Breakeven point Stationary point Even point None 9. If R = 5000 units / year, $C_{1}$= 20 paise, $C_{3}$= Rs 20, then EOQ is 5000 100 1000 200 None 10. The maximum value of f(x)= sinx is 1 $\frac{\sqrt{3}}{2}$ $\frac{1}{\sqrt{2}}$ $\frac{-1}{\sqrt{2}}$ None 11. Marginal revenue of the demand function p= 20–3x is 20–6x 20–3x 20+6x 20+3x None 12. Relationship among MR, AR and $ \eta_{d}$ is $\eta_{d}=\frac{AR}{AR-MR}$ $\eta_{d}=AR-MR$ MR=AR$=\eta_{d}$ $AR=\frac{MR}{\eta_{d}}$ None 13. For the cost function C $=\frac{1}{25}e^{5x}$, the marginal cost is $\frac{1}{25}$ $\frac{1}{5}e^{5x}$ $\frac{1}{125}e^{5x}$ $25e^{5x}$ None 14. If demand and the cost function of a firm are p= 2–x and C=$2x^{2}+2x+7$, then its profit function is $x^{2}+7$ $x^{2}-7$ $-x^{2}+7$ $-x^{2}-7$ None 15. Profit P(x) is maximum when MR = MC MR = 0 MC = AC TR = AC None 16. If the demand function is said to be elastic, then $\begin{vmatrix} \eta_{d } \end{vmatrix}> 1$ $\begin{vmatrix} \eta_{d } \end{vmatrix}= 1$ $\begin{vmatrix} \eta_{d } \end{vmatrix}< 1$ $\begin{vmatrix} \eta_{d } \end{vmatrix}= 0$ None 17. Average fixed cost of the cost function C(x)$=2x^{3}+5x^{2}-14x+21$ is $\frac{2}{3}$ $\frac{5}{x}$ $\frac{-14}{x}$ $\frac{21}{x}$ None 18. If the average revenue of a certain firm is Rs. 50 and its elasticity of demand is 2, then their marginal revenue is Rs. 50 Rs. 25 Rs. 100 Rs. 75 None 19. The elasticity of demand for the demand function x $=\frac{1}{p}$ 0 1 $\frac{-1}{p}$ $\infty$ None 20. Instantaneous rate of change of y=$2x^{2}+5x$ with respect to x at x=2 is 4 5 13 9 None Time's upRelated Posts:Chapter 1: Applications of Matrices and DeterminantsChapter 1: Introduction to Micro EconomicsChapter 2. Consumption AnalysisChapter 3: Production Analysis
Leave a Reply